Overview. Lecture 13: Graphics and Visualisation. Graphics & Visualisation 2D plotting. Graphics and visualisation of data in Matlab

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1 Overview Lecture 13: Graphics and Visualisation Graphics & Visualisation 2D plotting 1. Plots for one or multiple sets of data, logarithmic scale plots 2. Axis control & Annotation 3. Other forms of 2D plots: charts, histograms Graphics and visualisation of data in Matlab There will be many occasions where you will use a computer, not to perform calculations on data, but rather just to visualise some data. Often the appropriate visualisation will be easy to choose, but in more complex cases a basic understanding of the human visual system is important for designing a successful visualisation of the data. Simple 2D plotting that you already familiar with >> plot(x, y); % Plots the vector y versus the vector x. >> plot(y); % Plots the elements of vector y versus % their indices. % If y is complex this is equivalent to % plot(real(y), imag(y)). >> plot(x, y, s); % Plots the vector y versus the vector x % using markers to represent the data % points. The markers used are controlled % by the character string s. s is made up % of up to 3 (or 4) characters: % - a character denoting a colour r(ed), % y(ellow), b(lue), etc. % - a character denoting a symbol to use % at each coordinate:. (point), % o (circle), * star, v (triangle), etc. % - a character denoting the line style % between coordinates: - (solid), % : (dotted), -. (dashdot), -- (dashed). 1

2 Plotting several data sets on one set of axes >> plot(x1, Y1, X2, Y2, X3, Y3,...); % Plots Y1 versus X1, Y2 versus X2, Y3 versus X3, etc. >> plot(x1, Y1, S1, X2, Y2, S2,...); % As above, but with plotting specification strings % for each data set. Example: >> plot(x, Y, 'y--', X, Y, 'go'); % Plots the data twice: first as a yellow dashed line, % then with green circles at the data points. Plotting in logarithmic scales >> semilogx(x, y); % The same as plot(x, y) but with a % log (base 10) x-axis scale. >> semilogy(x, y); % The same as plot(x, y) but with a % log (base 10) y-axis scale >> loglog(x, y); % The same as plot(x, y) but with a % log scale on both axes. Be on the lookout for occasions when logarithmic plots are more appropriate for your data. Cases when you might want to use logarithmic plots: When there is a very large range of magnitudes in your data. When the ratio of data values relative to each other are more important than their absolute magnitudes. When you are seeking to show that the relationship between two variables follows some power law. A plot of a power function should produce a straight line on log axes. Example For example, assume we have the following function: y = a*x 3 Taking the log of both sides produces: log(y) = log(a) + 3*log(x) which is a straight line with slope of 3 and a y intercept of log(a). 2

3 Axis control Matlab generally does a fairly good job of automatically scaling axes to suit the data. However, you can set the axis range yourself with the axis function: >> axis([xmin, xmax, ymin, ymax]); Note that the argument supplied to axis is one vector. Cases when you might want to set the axes manually: When you want to ensure that the y-axis range starts at zero and not at the minimum value in the array of y values. When you are generating two or more plots side by side for comparison and you want to ensure that both plots have the same axis ranges. More on the axis command The axis command can do other useful things. For example, >> axis equal; % Makes axis increments equal on both axes. % This preserves the geometry of shapes and % prevents them from appearing distorted. >> axis off; % Removes the axes from the plot. Type help axis at the Matlab command prompt to learn more about the axis command. Graph annotation You should always label all axes in a plot and annotate the plot with a title. The title function is used to generate a plot title. >> title('the plot title'); The xlabel and ylabel functions are used to label the x and y axes respectively. >> xlabel('x axis label'); >> ylabel('y axis label'); Display the units of measurements used on each axis. You can place text at a specified location with the text function. >> text(3, 4, 'The point (3,4) is very interesting'); The legend function The legend function is used to provide legends for each data set that have been displayed simultaneously on one set of axes via the plot(x1, Y1, X2, Y2, X3, Y3,...) function. For example: >> legend('label 1', 'Label 2',..., 'Label N'); % Adds a legend for each data set in the plot. Type help legend at the Matlab command prompt to learn more about the many options available with this function. 3

4 Creating and switching between figure windows The figure function is used to control different figure (or plot) windows. >> figure; % Creates a new figure window. % This becomes the "current" figure. >> figure(n); % Makes figure N the current figure window. % This function creates a new figure window % called N if N does not already exist. >> delete(n); % Deletes figure N. Multiple plots within the one figure window You can divide a figure window into a grid and place subplots within individual grid cells. The subplot command is used to break a figure window into a grid: >> subplot(noofrows, NoOfCols, CellNo) This function divides the figure window into NoOfRows rows and NoOfCols columns. The cells are numbered from left to right, top to bottom. After breaking the figure window into cells, the subplot function makes the cell numbered CellNo the "active" cell. The active cell "receives" all subsequent plotting commands. Example For example, imagine generating two plots one above the other: Another example >> xs = 0 : 0.1 : 10; >> subplot(2, 1, 1), plot(xs, sin(xs)), xlabel('x'), ylabel('sin(x)'); >> subplot(2, 1, 2), plot(xs, cos(xs)), xlabel('x'), ylabel('cos(x)'); >> subplot(2, 1, 1), plot(x1, y1), title('plot 1'); % The first call to subplot breaks the figure window into % 2x1 cells, making the top one the active cell. >> subplot(2, 1, 2), semilogy(x2, y2), title('plot 2'); % A second call to subplot is needed to plot to the % second cell. 4

5 Other forms of 2D plots You can plot 2D data in many different forms: >> bar(x, y); % Creates a bar graph. Values in array x % are used to label each bar. % Values in array y are used to determine % the height of each bar. >> pie(x); % Creates a pie graph. The values in % array x are converted into percentages % so that their sum is 100%. >> hist(x, nbins); % Plots a histogram. The values in % array x are divided into nbins bins. % The number of data values that fall % in each bin are then plotted. % This function can also return the bin % frequencies. 5